Follow the Math!: The mathematics of quantum mechanics as the
mathematics of set partitions linearized to (Hilbert) vector spaces
- URL: http://arxiv.org/abs/2208.00384v1
- Date: Sun, 31 Jul 2022 07:45:17 GMT
- Title: Follow the Math!: The mathematics of quantum mechanics as the
mathematics of set partitions linearized to (Hilbert) vector spaces
- Authors: David Ellerman
- Abstract summary: The math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions.
The key machinery to go from indefinite to more definite states is the partition join operation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The purpose of this paper is to show that the mathematics of quantum
mechanics (QM) is the mathematics of set partitions (which specify
indefiniteness and definiteness) linearized to vector spaces, particularly in
Hilbert spaces. That is, the math of QM is the Hilbert space version of the
math to describe objective indefiniteness that at the set level is the math of
partitions. The key analytical concepts are definiteness versus indefiniteness,
distinctions versus indistinctions, and distinguishability versus
indistinguishability. The key machinery to go from indefinite to more definite
states is the partition join operation at the set level that prefigures at the
quantum level projective measurement as well as the formation of
maximally-definite state descriptions by Dirac's Complete Sets of Commuting
Operators (CSCOs). This development is measured quantitatively by logical
entropy at the set level and by quantum logical entropy at the quantum level.
This follow-the-math approach supports the Literal Interpretation of QM--as
advocated by Abner Shimony among others which sees a reality of objective
indefiniteness that is quite different from the common sense and classical view
of reality as being "definite all the way down."
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